Q5) (a) Solve by using Laplace transform the partial differential equation 8², =9. y(0,t)= 0, y(2,t) = 0, y(x,0) = 20 sin 2x-10 sin 5mx and " dy(x,0) Ət =0

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Solve the simultaneous ODES (a) (b) y"(t) + y'(t)- 2y(t) = sin t., x'(t) + x(t)- 3y(t) = 0 -

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Q: Solve the linear differential equation using Fourier transform.

A: The objective of this question is to solve the given linear differential equation using the Fourier…

Q: Consider the Bernoulli equation y' + -y = 3y°. After applying an appropriate substitut this equation…

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Q: x-1, X)1 find the generol solution of the differential eguation below

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Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: x· y'+xy=0 (>0): y(0) = 0, y'(0) = 0, y" (0) = (g) ey"+sin x y" + cos x I .

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Q: Verify that y(t)=C_(1)sin5t+C_(2)cos5t is a solution of y''(t)+25y(t)=0

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Q: Solve using Laplace Transfrom Method: y'''+3y''+3y'=y       y(0)=7,   y'(0)=-7,    y''(0)=11

A: Given function is, y'''+3y''+3y'=y    y(0)=7,   y'(0)=-7,    y''(0)=11 Now, using the…

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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Q: Solve using homogeneous differential equations

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Q: Use the inverse differential operators to solve the initial value problem: 2y'' + 5y' + 2y = e2x

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Q: use the method of frobenius to find solution for the given equation x²y'' - 2(x + x²)y' + (x² + 2x…

A: Given differential equation is x2y''-2(x+x2)y'+(x2+2x+2)y=0          (1) Comparing with general…

Q: Q5) find the derivative 1. x = sin and y = sin+ cos if taken together, satisfy the differential…

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Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

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Q: Solve the nonhomogeneous equation? .3. x*y" + x²y" – 2xy' + 2y = x³ In x. -

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Q: Q.12) The solution of y" + y' = 0 by using power series method , is! %3! a) y(x) = a, – a,(1-+ b)…

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Q: Q.1) The general solution of the equation e' cos , is:

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Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

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Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

Q: Solve the ODE with differentials operator (D²+4)y= cos(2x) + cos (4x)

A: Linear ordinary differential equation

Q: Consider the differential equation 4y' = 3y + 2x/y Which of the following is the linear form of this…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

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